A point with integral coordinates is called a lattice point. For example, is a lattice point, whereas is not. How many lattice points lie on the graph of ?Source: NCTM Mathematics Teacher, January 2006

Solution
The graph of is a circle with center at and radius . Any lattice point on the circle must form a Pythagorean triple with the radius. Since is a Pythagorean triple, is a lattice point on the circle.
From this initial lattice point we derive seven other lattice points by a series of reflections across the axes for a total of eight.
Quadrant I:
Quadrant II:
Quadrant III:
Quadrant IV:

Plus the four special lattice points . lattice points lie on the graph of .